There are n boxes C1, C2, . . . , Cn in 3D space. The edges of the boxes are parallel to the x, y or z-axis. We provide some relations of the boxes, and your task is to construct a set of boxes satisfying all these relations. There are four kinds of relations (1 ≤ i,j ≤ n, i is different from j): • I i j: The intersection volume of Ci and Cj is positive. • X i j: The intersection volume is zero, and any point inside Ci has smaller x-coordinate than any point inside Cj. • Y i j: The intersection volume is zero, and any point inside Ci has smaller y-coordinate than any point inside Cj. • Z i j: The intersection volume is zero, and any point inside Ci has smaller z-coordinate than any point inside Cj. Input There will be at most 30 test cases. Each case begins with a line containing two integers n (1 ≤ n ≤ 1,000) and R (0 ≤ R ≤ 100,000), the number of boxes and the number of relations. Each of the following R lines describes a relation, written in the format above. The last test case is followed by n = R = 0, which should not be processed. Output For each test case, print the case number and either the word ‘POSSIBLE’ or ‘IMPOSSIBLE’. If it’s possible to construct the set of boxes, the i-th line of the following n lines contains six integers x1, y1, z1, x2, y2, z2, thatmeansthei-thboxisthesetofpoints(x,y,z)satisfyingx1 ≤x≤x2,y1 ≤y≤y2,z1 ≤z≤z2. The absolute values of x1, y1, z1, x2, y2, z2 should not exceed 1,000,000. Print a blank line after the output of each test case. Sample Input 32 I12 X23 33 Z12 Z23 Z31 10 00 Sample Output Case 1: POSSIBLE 000222 111333
2/2 888999 Case 2: IMPOSSIBLE Case 3: POSSIBLE 000111